Keywords: material point method, surface tension, boundary conditions, heat equation
Abstract: We will present the results of several recent works on incorporating surface tension and thermodynamic effects into the material point method. On both fronts, a key innovation is a novel boundary quadrature method for MPM surfaces. We will explain how these methods can be made conservative (e.g., for momentum and heat), and we will demonstrate a number of interesting examples from both computational physics and computer graphics. Our methods are able to simulate a dynamic range of phenomena---from thermocapillary effects like Marangoni convection, to high-surface tension fluids like liquid metals, to thin-film effects similar to tears of wine---that are typically quite difficult to achieve with other numerical methods. We will conclude with some thoughts on generalizing these ideas to other MPM simulation problems.